Path integrals, the ABL rule and the three-box paradox

TL;DR

This paper analyzes the three-box paradox using path integrals and the ABL rule, revealing how interference and measurement choices create paradoxical features that can be mimicked classically with non-local perturbations.

Contribution

It demonstrates that the ABL rule is a special case of Feynman's probability assignment and clarifies the paradox by linking it to measurement-induced interference effects.

Findings

The ABL rule is a specific case of Feynman's probability method.

Paradoxical features arise from attributing properties across different measurement ensembles.

Classical systems can mimic quantum paradoxes with non-local perturbations.

Abstract

The three-box problem is analysed in terms of virtual pathways, interference between which is destroyed by a number of intermediate measurements. The Aharonov-Bergmann-Lebowitz (ABL) rule is shown to be a particular case of Feynman's recipe for assigning probabilities to exclusive alternatives. The 'paradoxical' features of the three box case arise in an attempt to attribute, in contradiction to the uncertainty principle, properties pertaining to different ensembles produced by different intermediate measurements to the same particle. The effect can be mimicked by a classical system, provided an observation is made to perturb the system in a non-local manner.